And yet it still grates on my ears every time someone uses it in the singular. But the same things happens when someone ends a sentence with a preposition or splits an infinitive, and neither are those consider grammatical faux pas anymore.
That is true, but ending sentences with prepositions still makes you sound like you don't know how to English. "Where are you at?" Just no. Why add the extra word that doesn't clarify anything? "Where are you going to?" Even writing it makes me cringe. Granted, if doing otherwise would make the sentence sound awkward, go for it. e.g. "Ending sentences with prepositions? That is something up with which I will not put!" I am such a pedantic nerd that I still write that way and try to find a way to make it sound less awkward.
Every time? If a person never used it I think he or she might sound stilted, since he or she would need to alter his or her speech in order to avoid the pronoun he or she wanted to avoid.
When I was in academia, it was considered acceptable for one to alternate between his and her when the gender of the subject is unknown. Using his or her every time does sound stilted, but proper grammar often sounds "weird". My highschool English teacher's favorite phrase was "things that 'sound right' are often wrong". That's the beauty of this fucked up language. I refuse to believe that masculine pronouns being the default gender neutral is some conspiracy by the patriarchy, but that's just me.